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Butterfly IVb.15.Cβ

From Šuvakov & Dmitrašinović (2013). Sequences of orbits from the Belgrade three-body gallery.

Butterfly IVb.15.Cβ is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 68.038 time units, published by Šuvakov & Dmitrašinović (2013). A second butterfly sequence with a different topology from class I. It is weakly unstable (largest Floquet multiplier 1.007), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000887 of each other at a top speed of 33.6, line up 106 times a period, and the computed loop closes to 7.1×10⁻²⁶.

Measured over one period

Period: 68.03772396
Masses: 1 : 1 : 1
Energy: -1.72424
Angular momentum: 0
Closest approach: 8.9×10⁻⁴
Top speed: 33.57
Path length: 174.73
Alignments per period: 106
Topology: ababABAbabaBABababABAbabaBABababABAbabABABabaBABAbabABABabaBAB (free-group class)
Stability: weakly unstable (|λ|max 1.007)
Loop closure: 7.1×10⁻²⁶

Neighbours on the map

All Butterfly IVb orbits, the families of periodic three-body orbits, or the atlas map.